Unless one has very good posture, the cervical spine doesn't like compression. Most weight trainers have a pretty significant forward head posture, which already loads the c-spine more than it is designed for. Add ballistic compressive loading to this, expect degenerative changes sooner rather than later.

Train the neck for isometric strength, IMO, much like the lower back. C-spine is very much like the lumbar, better to train for stability than mobility, best to minimize compressive loading and shear (especially ballistic). If I wanted to add neck strength training to my regimen, I'd likely just get the Everlast (?) head weight and wear it during sets of my gymnastics-type isometric holds (ie. front/back levers, etc.).